Backanálisis

A Practical Procedure for the Back Analysis

of Slope Failures in Closely Jointed Rock

MassesH. SONMEZR. ULUSAYC. GOKCEOGLU

Where closely jointed rock masses are encountered in slopes, failure canoccur both through the rock mass, as a result of combination of macro andmicro jointing, and through the rock substance. Determination of thestrength of this category of rock mass is extraordinarily dicult since thesize of representative specimens is too large for laboratory testing. This di-culty can be overcome by using a non-linear rock mass failure criterion orby back analysis of such slopes to estimate the rock mass strength. In thispaper, a practical procedure and a computer program are presented for theback determination of shear strength parameters mobilized in slopes cut inclosely jointed rock masses which obey a non-linear failure criterion ratherthan a linear one. The procedure shows that the constants to derive normalstress dependent shear strength parameters of the failed rock masses can bedetermined by utilizing a main cross-section and without a pre-determinedvalue of rock mass rating (RMR). Trials are made for dierent RMRm andRMRs values corresponding to various possible combinations of the constantm and s, which are used in the HoekBrown failure criterion, satisfying thelimit equilibrium condition. It is also noted that the procedure provides aquick check for the rock mass rating obtained from the site investigations.The method is used in conjunction with the Bishops method of analysisbased on circular slip surfaces. The procedure outlined in this paper has alsobeen satisfactorily applied to documented slope failure case histories in threeopen pit mines in Turkey. # 1998 Elsevier Science Ltd.

INTRODUCTION

In a rock mass with clearly defined discontinuity sets,failure mechanisms related to discontinuities can beanalyzed and the stability of slopes excavated in thatrock mass can be calculated providing the shearstrength along the discontinuities is known. However,such an analytical approach might not be feasible forslopes containing multiple discontinuity sets with largevariations in mechanical characteristics. Continuumcalculations for engineering structures in or on a rockmass, whether analytical or numerical, cannot beappropriate, since over-simplifications result from pre-senting the rock mass as a continuum.

In general, the slope stability determination methodsdepending on the material involved may be dividedinto three broad categories:

(a) Methods suitable for slopes in soils or soil like

materials where the strength of the material can bedetermined from testing small specimens of the ma-

terial in the laboratory.

(b) Methods suitable for slopes in hard jointed rocks

where slope stability is controlled by the discontinuities

in the rock material. The potential for failure is depen-dent on the presence and orientation of discontinuities,

and shear strength along them.

(c) Methods suitable for closely jointed rock masses

where failure can occur both through the rock mass,

as a result of a combination of macro and micro joint-ing, and through the rock substance. Determination of

the strength of this category of rock mass is a much

more dicult task. There are formidable diculties inthe sampling and testing of undisturbed samples that

are suciently large to represent the combined eectsof rock material and discontinuities. The possibility for

the measurement of the shear strength of such rock

masses is usually based on some form of classification

Int. J. Rock Mech. Min. Sci. Vol. 35, No. 2, pp. 219233, 1998# 1998 Elsevier Science Ltd. All rights reserved

Printed in Great Britain0148-9062/98 $19.00+0.00PII: S0148-9062(97)00335-5

Hacettepe University, Faculty of Engineering, GeologicalEngineering Department, Applied Geology Division, 06532Beytepe, Ankara, Turkey.

219

techniques [13] in conjunction with a non-linear fail-ure criterion [48].A rock mass is described as closely jointed when the

joint spacing is small in relation to the scale of theproject in question. In closely jointed media it seemsappropriate to assume that the material is approxi-mately isotropic and homogeneous, i.e. there are noclearly defined joint planes or joint sets which controlthe form of the failure mode. In these rocks, the jointspacing is a fraction of meter, the individual particlesof rock mass are very small compared to the dimen-sion of slope and these particles are not interlockeddue to their shape. Depending on the number andnature of the discontinuities, the intact rock pieces willtranslate, rotate or crush in response to stressesimposed on the rock mass. The behavior of the mass isthus a consequence of the combined action of a largenumber of individual joints. When the rock mass con-tains a number of discontinuity sets, having relativelysmall spacings in relation to the slope size, failure canoccur along a shear surface similar to those observedin soil slopes. Therefore, the required conditions for acircular failure are mostly satisfied in heavily jointedrock masses as illustrated in Fig. 1.The standard method for assessing the strength of a

geotechnical material is to recover a sample and test itin laboratory. In the case of a closely jointed rockmass it is clearly not possible to recover a sample thatis large enough to represent the joint system.Therefore, an empirical approach such as rock massclassification can be attractive alternative, providedthat the appropriate parameters are included in theclassification system. In order to overcome the dicul-ties in laboratory determination of the shear strengthof jointed rock masses; the HoekBrown failure cri-terion in conjunction with geomechanics classificationsystem [1] is commonly used.Rock mass classification has been applied success-

fully in tunnelling and underground mining [13, 9]. Anumber of systems, introduced by Bieniawski [1] andby Romana [10], has also been suggested for rockslopes. It should be noted, however, that the use ofrock mass classifications developed particularly forunderground works may lead to unsatisfactory results

when applied to near-surface applications such as rockslopes. This is due to the restrictions of these systemswhich are not well considered.Recently, an empirical failure criterion developed by

Hoek and Brown [58] has been adopted to the RMRrock mass classification scheme [1] to assess the shearstrength of the jointed rock masses in surface andunderground excavations. This approach has been alsoemployed in slope stability analyses by severalinvestigators [1114]. The slope mass rating (SMR)classification scheme proposed by Romana [10] alsoinvolves the input parameters used by the RMR-sys-tem, but generally provides assessments on structurallycontrolled slope failures.The main input parameters used in various classifi-

cation systems are more or less the same. Namely,these systems consider intact rock strength, RQD, dis-continuity spacing, condition and orientation of dis-continuities and groundwater conditions. Although anumber of additional input parameters and somemodifications are required in the RMR classificationscheme, the advantage of the system is that it providesan easy connection to the HoekBrown failure cri-terion for jointed rock masses. The intact rock strengthis one of the input parameters involved in the RMR-System and is only of limited interest with regard tothe stability of rock slopes in which failure is mostoften associated with the shear strength of discontinu-ities. Sometimes a rock mass having low intact rockstrength is a consequence of the failed rock containinga large number of discontinuities. In addition to this,the purpose of including intact rock strength in theclassification system for slopes is to give an assessmentof wall rock strength of the discontinuities. As statedby Hoek [15], the HoekBrown failure criterion is onlyapplicable to intact rock or to closely jointed rockmasses which can be considered homogeneous and iso-tropic. The rock mass parameters RQD and disconti-nuity spacing define the block size and block form andare also very useful in analyzing stability of slopes.Therefore, these two parameters are considered by theauthors to be the parameters of meaningful value inrock mass classification, particularly for slopes exca-vated in closely jointed rock masses.

Fig. 1. Eect of scale on rock strength and possible mechanisms of failure in rock slopes.

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES220

The condition of discontinuities includes the itemsrelated to roughness, continuity, infill material, aper-ture and degree of weathering. Laubscher [9] takesinto account in his final RMR rating only the con-dition factor of the most prominent discontinuity setor the discontinuity set with the most adverse influenceon the stability of an underground excavation. This istoo simple for slopes where the failure is often notdetermined by one main discontinuity set. Particularlyfor the slopes in a closely jointed rock mass, the con-dition rating becomes more important and it is takenas the mean value of the condition ratings of thedierent discontinuity sets. For the rock slopes, thepersistence has a considerable influence on the stabilityand the RMR-System takes into account the persist-ence as a quantitative factor. Weathering aects thecondition of discontinuities and discontinuity spacing.It is also noted that the state of weathering is con-sidered to be a local feature which has changed therock mass at a particular location. Within the lifespanof a cut slope, future weathering might lead to instabil-ity. Therefore, the weathering parameter included inthe RMR-System is a very important factor in slopestability.

The main problem of water in slopes is the pressureof the water in discontinuities. The presence of waterin discontinuities reduces the stability of slopes byreducing the strength of discontinuity surfaces or ofany infill material. The water pressure is taken intoaccount in the slope stability analysis by estimating thepressure or the position of groundwater table in slope.But the softening or weakening eect of water on dis-continuity surfaces becomes more important for slopes.Consequently, the groundwater rating is an integralpart of the rock mass classification and should beassigned for each particular outcrop for slopes.In closely jointed or crushed rock masses it is very

dicult or impossible to determine the orientation ofdiscontinuities. In such cases, the orientation is notmeaningful, because part of the rock mass will fall intothe underground opening and require immediate sup-port regardless of discontinuity orientation. In the caseof slopes excavated in such rocks, the situation is notdierent. Bieniawski [1] in his RMR classificationscheme, suggests rating adjustments for discontinuityorientations, relative to proposed slope orientation,ranging between 0 and 60. No guidelines have beenpublished for the definition of each adjustment values,and no reference is given by Bieniawski to use of theRMR classification in slopes. The reason for this lackof use is probably the extremely high values of theadjustment rating values which may sometime result innegative RMR values. Therefore, the ratings assignedfor discontinuity orientation adjustments suggested byBieniawski [1] is unrealistic. Singh and Gahrooee [16]proposed better and clearer descriptions for disconti-nuity orientation in slopes. This approach was quanti-fied on the basis of rating with regard to the numberof possible modes of failure. The authors of the pre-

sent paper think that the above mentioned rating sys-tem is still questionable. First of all, Singh andGahrooee [16] did not change the values of ratingswhich can reach up to 60 points out of 100. As dis-cussed before, such an adjustment is not applicable inpractice. Secondly, in a closely jointed rock mass, themost probable mode of failure occurs in the form of acircular shape regardless of discontinuity orientation.Consequently, only one definition namely one poss-ible mode of failure is considered to be more logical,and a single adjustment of 5 for discontinuity orien-tation is more realistic for slope failures in closelyjointed rock masses.

Some factors such as method of excavation, majorplanes of weakness or change in stress are treated aslocal features which have influenced the rock mass at aparticular location and are not rock mass constants.These have been discussed by Laubscher [9],Romana [10] and Kendorski et al. [17]. The greatestinfluence of the method of excavation will be on thespacing of discontinuities. Depending of the blastingdamage, blasted slopes may have closer discontinuityspacing than natural slopes. Therefore, in order tocompensate for the influence of such local factors,necessary adjustments [1, 9, 17] are taken into consider-ation in rock mass classification for the slope failuresin closely jointed rock masses investigated in thisstudy.

On the other hand, during a classification process,serious diculties are encountered in determining ordescribing some of the rock mass parameters, particu-larly in poor quality rock masses [1820]. Due to suchuncertainties, the calculated rock mass rating mayerroneously aect the constants and shear strengthparameters derived from the non-linear rock mass fail-ure criterion. The most reliable way to obtain a meanvalue of the constants m and s employed by theHoekBrown failure criterion in an extended slope isby back-calculation and by comparison of the resultsof back-calculation with the available data derivedfrom the HoekBrown criterion [21]. However, insome cases it is unlikely that an accurate assessment ofthe true strength parameters for a given rock mass willever be available due to limitations, so RMR valuescannot be precisely determined. Because the results ofback-analysis provide a range of combinations ofapparent friction angle and cohesion, the problem ofparameter selection becomes dicult in such cases.

The procedure presented herein is to perform aback-analysis of failed slopes cut in jointed rockmasses to estimate the rock mass rating and shearstrength parameters mobilized at the time of failure.The main philosophy of the method recognizes that itis unlikely that an accurate assessment of the value ofRMR and shear strength parameters for a given rockmass will ever be available. A detailed description ofthe procedure which can be readily incorporated intothe conventional back analysis of a slope failure in ajointed rock mass, where only a single cross-section is

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES 221

available, is presented with a computer solution devel-oped for the purpose. The proposed method is alsoapplied to failure case histories in jointed rock massesat three open pit mines located in Turkey to check itsperformance.

METHOD OF ANALYSIS

Theoretical background-basic procedure

One of the most dicult tasks in slope stabilityanalysis is the determination of the shear strength par-ameters (c, f) along the sliding surfaces. In geotechni-cal engineering practice, failure of a slope can beregarded as a full scale field test and an assessment ofany failure is, therefore, of considerable value.Appropriate geomechanics models can be used to esti-mate the values of shear strength parameters on thebasis of certain assumptions. These back calculatedvalues may then be used for preventative and remedial

work for the redesign of failed slopes and for new pro-

jects in similar types of material. Therefore, it is con-

sidered that back analyses are an integral part of the

slope design.

The shear strength parameters of a failed slope have

been back calculated by geotechnical engineers and en-

gineering geologists in the following procedures:

(a) Assuming the value of the angle of internal fric-

tion f or of the cohesion c to calculate another [22](Fig. 2(a)).

(b) Utilizing a main cross-section of a failed slope

and another cross-section near the main one in the

same failed slope or utilizing two cross-sections in two

failed slopes which have similar geological and hydro-

geological conditions to establish two equations and

then evaluate the values of c and f (single solution;Fig. 2(b)).

(c) Because of the variations in the mechanical prop-

erties of the same material in dierent places, utilizing

Fig. 2. Basic back analysis approaches applied for the slope forming materials obeying linear failure envelopes: (a) derivedrange of c and f and determination of c from an assumed f; (b) single solution for two slides with dierent geometry; (c)multiple solutions for four slides with dierent geometry; and (d) multiple solutions with a comparison with laboratory de-

rived strength test results.


more than two slope cross-sections to obtain as manyas n(n 1)/2 points of intersections (solutions) for ncurves c(f) (multiple solutions; [23]; Fig. 2(c)). The setof continuous curves represents the range of back cal-culation solutions from which the most realistic sol-ution can be obtained based on engineering judgement,experience and verified with shear test results if theseare available (Fig. 2(d)).

The above procedures, however, are based on theback calculation of the shear strength parameters ofthe materials obeying linear MohrCoulomb failurecriterion which are characterized by c and f valuesindependent from the normal stress. But a consensushas gradually emerged among the rock mechanicscommunity that the failure envelope for a closelyjointed rock mass is curved rather than linear. Theauthors believe that the HoekBrown non-linear fail-ure criterion [47], which has gained an increasingpopularity in stability analyses made in conjunctionwith rock mass classification systems, provides a mean-ingful estimate of rock mass behavior. Due to the non-linear nature of this failure criterion, the above men-tioned methods are unrealistic for use with closelyjointed rock slopes, i.e. the shear strength parametersof a failure surface in closely jointed rock masses canbe calculated for any specific normal stress value usingthe material constants (m and s) as a function of rockmass rating (RMR) from the following equation [24];for disturbed rock masses:

m

mi exp

RMR 100

14

1a

s expRMR 100

6

1b

for undisturbed or interlocking rock masses:

m

mi exp

RMR 100

28

2a

s expRMR 100

9

2b

where mi is the material constant of intact rock sampleand can either be calculated form laboratory triaxialtest on intact samples or taken from the tables pro-posed by Hoek [24], and Hoek et al. [8].

In the case of a slope instability with accuratelyspecified failure geometry in a closely jointed rockmass, if the value of RMR is precisely determined andthe triaxial test data are available, back analysis of thefailure provides a realistic comparison between therock mass strength obtained from the failure surfaceyielding a safety factor of unity and the failure envel-ope derived with the updated HoekBrown failure cri-terion as reported by Ulusay and Aksoy [21] (Fig. 3).However, in weak sedimentary rocks, such as shales,marls and siltstones, and in heavily fractured schistoserock masses, preparation of specimens for triaxial test-

ing can be very dicult because of tendency of these

materials to slake and de-laminate. In addition, as

reported by Unal et al. [18], Ulusay et al. [19] and

Unal [20], serious diculties are encountered in deter-

mining or describing some of the rock mass par-

ameters, particularly in weak, stratified and clay-

bearing rocks. In such circumstances overestimated

rock mass ratings might be obtained and they result in

deriving dierent m and s values than those in real

situation. On the other hand, in some areas where

slope failures have occurred, because of the limited

number of outcrops or no borehole data, the rock

mass rating can not be precisely determined.

Therefore, a back analysis based on such limited or

questionable data may yield unrealistic results.

The strategy of this study is aimed at overcoming

the diculties associated with the limitations discussed

above. In this strategy, a procedure is suggested to

identify the most reasonable and a common rock mass

rating (RMR) value which corresponds to the pair of

m and s satisfying the limit equilibrium condition. In

jointed rock masses obeying the HoekBrown failure

criterion, a function F, the conventional factor of

safety commonly specified in the limit equilibrium

methods of slope stability analysis, depends on several

variables and for any particular sliding surface may be

written in the following form:

F FfRMRm, s, GW, G g 3where RMR: rock mass rating (m and s are the ma-

terial constants), GW: groundwater conditions prevail-

ing in the slope, G: geometry of the slope and the

failure surface.

Fig. 3. Comparison between the rock mass shear strength obtainedfrom the failure surfaces yielding safety factors of unity and the fail-ure envelope with the updated HoekBrown criterion for coal-bear-

ing rocks (after Ref. [21]).


The real factor of safety F is considered to beknown and equal to one for a case study concernedwith a slope that has failed. The value of the geometrydata G in Equation (3) can be delineated from theresults of field inspection or by surveying the actualfailed slope. The values of the constants m and s at thetime of failure are unknowns and groundwater con-dition, GW, may be either known or unknown.The suggested approach involves the determination

of various possible combinations of m and s satisfyingthe following equation:

1 FfRMRm, s, GW, G g 4where G and GW are considered as known in the pro-cedure.The back analysis method presented herein is based

on the following assumptions:(1) The geometry of the slope before and after fail-

ure, the position of the sliding surface, and thegroundwater conditions are known.(2) The mechanism of the movement is known.(3) A condition of static equilibrium at the point of

failure (limit equilibrium) exists at the time of failure.(4) In closely jointed media, it seems appropriate to

assume that material is approximately homogeneous.(5) What is obtained by back calculation is a

weighed mean value of RMR and corresponding mand s values along the failure surface at the time offailure.(6) A set of relations between the RMR from the

Bieniawskis rock mass classification [1] and the con-stants given in Equations (1a)(b) and (2a)(b) areused in conjunction with the equations given by theupdated HoekBrown failure criterion [24].(7) Uniaxial compressive strength (sc) and the ma-

terial constant mi are the input parameters.The back analysis procedure starts with the fact that

the constants m and s of a given rock mass dependupon an RMR value (Equations (1a)(b) and (2a)(b)), and therefore, various possible combinations of(m, s) pairs at the time of failure (F= 1) can be de-rived from dierent RMR values. The procedurewhich performs back calculations for three unknownparameters can be carried out using the following al-gorithm.Step 1. One variable, RMR, out of three unknown

geomechanical parameters (RMR, m, s) is selected andthe second unknown, the constant s, is calculated bythe utilization of Equation (1b) or Equation (2b)depending on the condition of disturbance (blastedand/or excavated rock, or none) of the rock mass. TheRMR value selected to calculate the parameter s isdenoted by RMRs.Step 2. By utilizing the position of the sliding sur-

face, normal stress acting on each slice base is calcu-lated. Keeping the previously chosen RMRs value andthe corresponding RMR (RMRm) which lead a valueof safety factor of unity are calculated by trial anderror technique in conjunction with the equations

given by the updated HoekBrown failurecriterion [24].Step 3. Trials are made for dierent values of

RMRs(s) to obtain various possible combinations ofRMRs and RMRm satisfying the limit equilibrium con-dition.The results of the back analysis are best presented in

a RMRsRMRm function forms, i.e. RMRs plottedagainst RMRm considering each combination to leadto a value of the factor of safety F= 1 (Fig. 4). Allthe points (or RMR pairs) located on the curve indi-cate a safety factor of unity. Because the closelyjointed rock mass is an approximately homogeneousmaterial, it is logical to consider that the rock massmust have a unique RMR value from which a pair ofm and s representing a given rock mass can be derivedusing Equations (1a)(b) and (2a)(b). Thus, if astraight line passing from the origin of the graph (seeFig. 4) with an inclination of 458 is drawn, it intersectsthe RMRsRMRm curve at a certain point which indi-cates a common RMR (RMRRM:the actual RMR forthe rock mass) value for both constants at the time offailure and utilization of this back analyzed RMRRMvalue will yield the right combination of the two con-stants, m and s, of the rock mass.

Software description

The method described above has been used todevelop a computer program for conventional determi-nistic slope stability analysis and back calculation. Thecomputer program was written in QBasic and can runon any type of IBM PC or compatible equipped witha graphics card and monitor. The programHOBRSLP, which has routines that search the morecritical failure surface in a grid system or automati-cally, can handle slope stability analysis of circular slipsurfaces for slopes involving many benches with dier-ent geometries, various materials and dierent ground-water conditions, and includes simplified Bishopsmethod of analysis [25].Two options are included in the program: (a) con-

ventional stability analysis for searching the most criti-cal failure surface and corresponding lowest factor ofsafety; (b) back analysis of a failed slope with knownfailure geometry. Input data for the program includesthe coordinates of the points specifying slope geome-try, water conditions prevailing in the slope, and ma-terial properties. It will also prompt users to enter thetension crack position. Output consists of a table ofinput data, safety factor, a cross-section of the slopeshowing all strata, water table, the failure surface, anda list of ci, fi, sn, t for each slice base if the case con-sists of materials having non-linear failure envelopes.Three dierent methods of shear strength data inputare incorporated in the program with keyboard selec-tion of the input mode for conventional analysis.These three modes are as follows:(1) Input of the known shear strength parameters

derived from linear Coulomb equation.


(2) Calculating the shear strength parameters frominput data for rock types, RMR value, sc, and ma-terial constant mi.(3) Calculating the shear strength parameters from

normal stress (sn) acting on each slice base, and theconstants A and B for the materials fitted to powercurve strength equation (t= AsB).The back calculation option provides the use of the

first two modes mentioned above. In the back analysisoption, mi and sc are given as material properties withthe condition of rock mass (disturbed or undisturbed).The existing program can analyze slopes with up to150 slices. The steps to be followed during the ex-ecution of the program are shown diagrammatically inthe flow chart illustrated in Fig. 5.

EXAMINATION OF THE PROCEDURE ON ACTUALEXAMPLES

The procedure outlined above has been applied tofailed slopes in three open pit mines located in the wes-tern and central parts of Turkey (Fig. 6). All the slopespresented in the particular and well documented casehistories were cut in jointed rock masses where thejoint spacing is a fraction of a meter. It is, therefore,very much smaller than the scale of the cut slopeswhich are tens of meters high.

An externally loaded highwall slope failure (Case 1)

The particular case history presented and describedbelow is concerned with the instability of a highwall inEskihisar strip coal mine (YataganMugla) in south-western Turkey. No sign of instability in highwalls wasobserved until 1989. During a comprehensive slopestability research project by Ulusay [14], the highwallof the ninth slice was found to be unstable after load-ing the slope by a temporary spoil pile (Fig. 7).The failed highwall, located at the southern end of

the ninth slice, was excavated in the compact marlswhich lie above the coal seam with a thickness of 1520 m. In the failed highwall and in the entire pit, con-tinuous cross joints are well developed within the com-pact marl. Except local deviations, there are threedominant joint sets developed parallel and/or subpar-

allel to the normal faults crossing the Tertiary depos-its. Excepting local deviations, three dominant jointsets dipping 758858 NE and SW were identified. Theirpersistence is high and reaches up to 8 m in someplaces. The presence of cross joints, faults and flatlying bedding planes result in a closely jointed rockmass. The groundwater level rises above the coal seaminto the compact marls and where seepage occurs ittends to decline toward the compact marlcoal seamboundary. Thus, the failed part of the investigatedslope was dry.

In the strip coal mine, the overburden rocks com-posed of the compact marls were evaluated based onBieniawskis 1989 classification [1]. The data requiredfor rock mass rating determinations were obtainedfrom the geotechnical logs recorded and the scanlinesurveys carried out in accordance with the proceduresuggested by ISRM [26]. Values of RMR for the rockmass were determined for a number of individual sec-tions from seven fully cored geotechnical boreholesconsidering drill-run lengths ranging between 1 to 3 m.In addition, a total of seven scanline sections were alsoevaluated. Joint systems show negative exponential dis-tribution. Mean joint spacing (x) and the average num-ber of joints per meter (l) of the rock mass werecalculated as 0.386 m and 2.59 m1, respectively. In thecompact marls overlying the coal, excepting occasionallaminated levels, spacing between bedding planes ran-ged 0.3 to 1 m. Discontinuity surfaces observed on thefaces of the benches were normally dry. However,moisture appeared in some places when the surfaceswere scraped by a geologist hammer. The ranges ofthe five main parameters employed in the determi-nation of RMR values are tabulated in Table 1. Asexplained in the first section, the adjustment rating fordiscontinuity orientation was quantified on the basis ofrating with regard to the number of possible modes offailure [16]. In this study, only one mode of failure, cir-cular failure through the rock mass, was consideredfor discontinuity orientation adjustment. Mining appli-cations include dynamic processes. In the studied pit acontrolled blasting with a slight damage to loosen theoverburden, compact marls, is made. For this con-dition, a blasting damage adjustment of 0.94 [17] tothe RMR values of the compact marls was assigned.Using the statistical methods, individual RMR valueswere assessed and then RMR values ranging between50 and 62 with a mean value of 53 were obtained. Dueto light blasting carried out in the compact marls toloosen the overburden, disturbed rock mass conditionis considered and the value of mi (9.87) for intact rockwas calculated by linear regression analysis on themeasured triaxial data pairs from the intact rock, andthe constants m and s were found to be 0.344 and0.0004, respectively [14]. To assess the various controlson slope movements, the development of mobilizedshear strength and the failure mechanism under the in-fluence of the loads exerted by the spoil pile wereinvestigated by Ulusay and Aksoy [21] using determi-

Fig. 4. Basic concept of the proposed back analysis technique.


Fig. 5. The flow chart for the proposed method of analysis code HOBRSLP.


nistic and numerical (FEM) methods. For this pur-pose, available monitoring record, structural data andgroundwater information were examined, and a rockmass shear strength envelope was derived from theHoekBrown criterion in conjunction with rock massclassification for the highwall material. Ulusay andAksoy [21] back analyzed the failure utilizing fourcross-sections and indicated that the updated HoekBrown failure criterion used with rock mass classifi-cation gives strength values equal to those obtained bythe mobilized strength curve, and results of the backanalyses confirm the applicability of the loaded slopemodel proposed for the case.

The procedure presented herein was applied to thecase summarized above. Taking into consideration theloaded slope model (symmetrical vertical triangularexternal loading condition), the programHOBRSLP [14] was modified by the authors to incor-porate external loading conditions (Fig. 8).Considering that the predicted (based on the site ob-servations and monitoring data) surfaces were con-firmed by the calculated failure surfaces [21], fourfailure surfaces given in Fig. 9 were employed in the

back analyses. A mean uniaxial compressive strength

of 4.15 MPa determined from 40 test specimens for the

compact marl, and average values of unit weight of

13 kN/m3 and 16 kN/m3 were utilized for the spoil ma-

terial (in-situ) and the compact marl, respectively.

For each cross-section, starting from an arbitrarily

chosen initial RMR value of 18 for the calculation of

the constant s, the values of the constant m and corre-

sponding RMRm which satisfy a factor of safety of

unity for the given failure surfaces are calculated. The

results of the analyses are plotted in the form of

RMRmRMRs graphs (Fig. 10). It is evident from

Fig. 10(a)(d) that common values of RMR for the

constants m and s along the failure surfaces in section

1-1' is 51, along section 2-2' is 52 and along section 3-3' is 53. The RMR values back calculated for four fail-ure surfaces are equal to or nearly identical to 53 and,

thus they confirm the average value of RMR (53)

obtained from the comprehensive geotechnical logging

and scanline surveys performed by Ulusay [14]. Shear

strength values calculated for the base of each slice

involved by the four failure surfaces confirmed by the

predicted surfaces (at F= 1 condition) were plotted

against normal stresses acting at the slice bases onto

the original failure envelope of the rock mass derived

from the HoekBrown failure criterion by utilizing an

average RMR value of 53 (Fig. 11(a)). This compari-

son indicates that the mobilized strength plots match

the original failure envelope of the investigated rock

and the method proposed gives identical results to

those obtained in a previous study by Ulusay and

Aksoy [21]. The resulting curvilinear failure envelopes

with RMR values of 5153 given in Fig. 11(b). Figure

11(b) suggest that failure envelopes for the range of

calculated normal stress levels (sn) in the back ana-

Fig. 6. Location map of the back analyzed case study sites.

Fig. 7. Initiation of the slide in the highwall externally loaded by a spoil pile (Case 1).


lyzed slope show negligible and/or slight dierenceswhich result from probably due to small variations inthe mechanical properties of the same rock in dierentplaces.

Slope failure in a closely jointed schist rock mass at abarite open pit mine (Case 2)

The Baskoyak mine at the central part of Turkey isan open pit mine operated for the extraction of barite.A comprehensive slope stability project was carriedout to determine the engineering properties of the rockmass, and to assess the failure mechanism and thealternatives for improving the overall stability between1987 and 1988, and the investigation was published byUlusay and Yucel [27].Based on the scanline surveys consisting of 90 schist-

osity and 160 joint measurements and geotechnicallogging of a borehole of 75 m deep, Ulusay andYucel [27] reported that the schists should be regardedas comprising two rock mass types. The first type con-sists of a schist rock mass heavily broken by closelyspaced discontinuities (Fig. 12), and the second type isa weathered schist in dierent degrees both in thehangingwall and footwall, particularly observed at the

middle and lower benches. The unit weight of theschists ranges between 17.2 kN/m3 and 28.5 kN/m3

with a mean value of 22.2 kN/m3. The uniaxial com-pressive strength of the intact rock determined on alimited number of specimens due to the diculties insample preparation was 5.2 MPa. Slope failures cover-ing a single bench or two benches were observed atthree locations in the pit. The failures were circularand one of them occurred in the closely jointed rockmass. Back analysis of the failures indicated that thecalculated sliding surfaces confirm the actual failuresurfaces delineated from the site measurements [27].No any sign of groundwater was encountered throughthe geotechnical and previously drilled boreholes andon the benches. Thus, the pit slopes was considered asdry for stability assessments. The overburden materialand the ore are removed by the excavators withoutany blasting.The rock mass parameters of the heavily broken

part of the rock mass are given in Table 1. Ulusay andYucel [27] declared an RMR value of 21 in theirreport based on Bieniawskis 1976 classification [28].However, the authors of this recent study also calcu-lated the RMR value of the rock mass based on 1989version of the RMR classification [1] using the par-ameters given in Table 1 for this case. In this calcu-lation a discontinuity adjustment of 5 consideringone mode of failure, mass failure, was assigned.Because the presence of discrete fault zones runningvery close to the failed slope, a major structure adjust-ment of 0.7 [17] was also considered to obtain finalRMR value. An RMR value of 20.6 which is identicalto that derived from Bieniawskis 1976 classificationwas obtained.Utilizing the well delineated circular slip surface il-

lustrated in Fig. 13 and the geomechanical parametersgiven above, the proposed method was applied to thefailure occurred in closely jointed part of the schists.Choosing an initial RMR value of 10 for the calcu-

Table 1. Range of parameters employed in rock mass classifications for three cases considered in the study

Parameter Range (mean)/description

case 1 case 2 case 3

Uniaxial compressive strength(MPa)

1.146.41 (4.15) 4.206.15 (5.2) 35.444.3 (40.2)

RQD (%) 3798 0 9095

Spacing of discontinuities (mm)joints: 250410 (386) bedding: 300

10003040 310390 (370)

Condition of discontinuities aperture 01 mm; very thin softcoating; planar-smooth surfaces;fresh/slightly weathered; high

persistence

aperture 13 mm; soft infilling;slickensided surfaces; highlyweatered; high persistence

apertures

lation of the constant s, the analysis was started. Thepairs of RMRm and RMRs which lead a value ofsafety factor of unity are plotted and then theRMRRM value which satisfies limit equilibrium con-dition for the constants of m and s is found as 21(Fig. 14(a)). Besides, on the basis of normal stressesacting at the bottom of 10 slices in the failed mass, the

rock mass shear strength values obtained from the fail-ure surface yielding F= 1 are plotted on the originalst curve derived from the updated HoekBrown cri-terion utilizing an RMR value of 21 (Fig. 14(b)).These results indicate that the back calculated RMRvalue and the mobilized shear strength plots match theRMR derived from site investigations, and the original

Fig. 9. Slope profiles, and the predicted and calculated failure surfaces employed in the back analyses for the loaded high-wall case (Case 1).

Fig. 10. Back analysis plots illustrating the derivation of RMRsRMRm pairs satisfying the limit equilibrium condition forthe slope profiles examined (Case 1).


failure envelope of the investigated rock mass. Thus, itis concluded that the procedure outlined above alsoyielded realistic results for this case.

A slope instability in a coal mine (Case 3)

As an example of the proposed method, back analy-sis on a typical instability was carried out inKisrakdere open pit mine which is located at Soma lig-nite basin (see Fig. 6). The necessary geotechnical datawere collected by the authors from this pit. The coalseam is generally 20 m thick, but becomes thinnertowards the basin margins where the failed slope islocated. Figure 15(a) shows the geometry of the slopein which a single thin coal seam with a thickness of4.5 m is overlain by a sequence consisting of compactmarl, and soft clay beds about 10 m thick. The obser-vations on the slope surfaces, measurements throughthe blast-holes, and the records of the previously

drilled holes in the vicinity of the investigated slope

indicated that the groundwater table lies below the

failed marly rock mass. As being in the first case, the

coal seam acts an aquifer, and therefore, the failed

slope is dry. Bedding planes dip into opposite direction

of the slope. The marly rock which forms the majority

of the sequence has a carbonate content considerably

higher than its clay content. The actual slip surface

was in circular shape, which was evident from the field

inspection and topographical measurements carried

out along the failure surface, and passed through the

compact marl rock mass and the clay, above the coal

seam. Because the thickness of the coal seam reduces

in this part of the pit, highly steep slopes were cut to

extract the coal. In addition to this application, it is

concluded that the presence of a weak and soft clay,

and the jointed nature of the marly rock in the

sequence made the failure easier. Scanline surveys were

carried out in the close vicinity of the failed slope to

collect data for the discontinuities and to assess rock

mass conditions. Three main joints moderately and

Fig. 11. (a) Comparison between the rock mass shear strengthobtained from the back analysis and the failure envelope derivedwith the HoekBrown criterion considering the average RMR value(53) for the rock mass; (b) failure envelopes based on empirical fail-ure criterion for mean and lower bound RMR values derived from

the proposed method (Case 1).

Fig. 12. A view from the schist rock mass heavily broken by closely spaced joints and schistosity planes at a barite open pitmine (Case 2).

Fig. 13. Slope geometry before and after failure and circular slip sur-face in closely jointed schist rock mass (Case 2).


closely spaced, and bedding planes in the marly

sequence resulted in a jointed rock mass.

In this study, Bieniawskis 1989 [1] classification

scheme was used and the data for the rock mass rating

determinations were obtained from the scanline sur-

veys carried out at twentyfive locations in the studied

pit. The range of the rock mass parameters determined

in this study is given in Table 1. It is also noted that a

discontinuity adjustment of 5 for the case of onemode of failure and a blasting damage adjustment of

0.90 for fair blasting carried out in the compact marls,

which have considerable higher strength when com-

pared to those mentioned in Case 1, were considered.

A histogram of RMR values based on the assess-

ment of the line survey data (Fig. 15(b)) has a normal

form which indicates that RMR values are concen-

trated between 42 and 44 with a mean value of 43.

The geotechnical properties of the marl and the clay

determined by an experimental program are listed in

Table 2.

Considering the similarities between engineering

behavior of the clays in this site and the clays in a

transition zone at Yatagan coal mine, which were back

analyzed by Ulusay and Doyuran [29], the residual

shear strength parameters of the clay given in Table 1were assumed to be used for back analysis. The pro-cedure presented was applied to the failed slope by uti-

lizing data available for the site for the assessment ofshear strength parameters of the jointed marly rockmass.

The results are presented as a plot of RMRs vs

RMRm (Fig. 16(a)). The method suggests that theRMRRM value satisfying limit equilibrium condition is42.5. The back calculated RMRRM value (42.5) con-

firms the actual RMR (43) previously determined bythe authors through the site investigations. It is alsoevident from Fig. 16(b) that there is a good agreement

between the back calculated shear strengths at the baseof slices and the failure envelope derived from theHoekBrown failure criterion utilizing the actual

RMR value of 43.

Fig. 14. (a) Back analysis plots illustrating the derivation of RMRsRMRm pairs satisfying the limit equilibrium condition for the failurein the schist; (b) comparison between the rock mass shear strengthobtained from the back analysis and the failure envelope derivedwith HoekBrown criterion utilizing the RMR value (21) determined

from the site investigation (Case 2).

Fig. 15. (a) Cross-section illustrating the geometry of the failed slopeand the position of the strata; (b) RMR histogram for the marly

rock mass (Case 3).


CONCLUSIONS

Conventional back analysis of slope failures can

provide functional relations between shear strength

parameters c and f for slopes of homogeneous ma-terials with linear failure envelopes provided all the

other parameters are known. But in closely jointed

rock masses shear strength determination, particularly

due to the scale eect, is very dicult. In addition,

such back analyses have limited practical application

because these rocks obey a non-linear failure criterion.

In this study, the diculty of determining the shear

strength of such rocks and applicability of rock mass

classification to rock slopes are explained and a practi-

cal procedure with a computer solution for the back

analysis of failed slopes is put forward as a means of

estimating the mobilized shear strength required toexplain existing states of stability.

This study is based on the conventional deterministicanalysis framework. However, the procedure outlined,

which is based on the HoekBrown failure criterion, issuitable for back calculations with a maximum of

three unknown parameters (RMR and the constants mand s), and requires iterations. The main emphasis in

this paper is the application of the method where noprocedure of direct strength or RMR measurement is

possible. The rock mass rating (RMR) of the rock andthe corresponding constants, m and s, satisfying limit

equilibrium condition can be readily obtained from agraphic representation of the possible range of sol-

utions.

Three examples have been given to illustrate the ap-plication of the method in practical geotechnical engin-

eering. In the application of this approach, it wasfound that the back calculated and predetermined

values of RMR with the constants m and s were iden-tical. However, it should be kept in mind that the

classification systems which have been mainly devel-oped for underground works may give unrealistic

results when applied to rock slopes if their limitationsare not well considered. Adjustment for the discontinu-

ity orientation is one of the most important question-able parameter in the RMR system when it is applied

to rock slopes. Particularly in closely jointed rockmasses, which obey the non-linear HoekBrown failure

criterion, slope failures occur only in the form of a cir-cular shape regardless of discontinuity orientation.

Therefore, in such rock masses expecting of one poss-ible mode of failure and assignment and adjustment

value of 5 for the discontinuity orientation seems tobe more realistic. This approach was also confirmed by

the results of the stability analysis. On the other hand,consideration of the factors such as method of exca-

vation, major planes of weakness and change in stresswhich influence the rock mass at a particular location

and thus an adjustment for these factors becomenecessary in rock mass classification applied to rock

slopes. It is also noted that the HoekBrown failurecriterion in conjunction with the RMR classification

system is only applicable to intact rock or to closelyjointed rock masses, otherwise unrealistic results may

be obtained.

Therefore, it is reasonable to conclude that the

method seems to be a practical tool for back analyzingof slopes in jointed rock masses and to check the rock

mass rating obtained from site and laboratory investi-

Table 2. Material properties employed in the black analysis of Kisrakdere open pit mine (Case 3)

MaterialUnit weight (kN/

m3)U.C.S. (MPa) mi cp (kPa) cr (kPa) fp (8) fr (8)

Marl rock mass 23.7 40.2 9.04 Soft clay 18.0 17.7 14.9 21 18cp, cr: Peak and residual cohesion, respectively.fp, fr: Peak and residual internal friction angle, respectively.U.C.S.: Uniaxial compressive strength.

Fig. 16. (a) Back analysis plots; (b) comparison between the backanalyzed shear strength and the failure envelope derived with the

HoekBrown criterion for an RMR value of 43 (Case 3).


gations. In other words, the method may lead to thedevelopment of possible modifications in describingthe rock mass parameters particularly for the slopes, ifnecessary.A better understanding of the mechanics of jointed

rock mass behavior is a problem of major significancein geotechnical engineering. The authors believe thatthe HoekBrown failure criterion provides a good esti-mate for the shear strength of jointed rock masses.However, the authors hope that the application of theproposed method on various failure case histories inthe future may lead to provide a better tool for moreprecise input data and to check the equationsemployed by the non-linear failure criterion.

AcknowledgementsThe authors express their gratitude to ProfessorEvert Hoek of Canada, and to Professor Hasan Gercek ofKaraelmas University, Turkey for their valuable comments and sug-gestions in preparing the manuscript.

Accepted for publication 26 November 1997

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